{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from bokeh.plotting import figure, show, output_notebook"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## algorithm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def probability(n):\n",
    "    # initial probabilities\n",
    "    p = [0, 0, 0, 0, 0, 1]\n",
    "    \n",
    "    # next field is conditioned on previous six fields\n",
    "    for _ in range(n):\n",
    "        p.append(sum(p[-6:]) / 6)\n",
    "\n",
    "    return p[6:]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## run"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "fields = probability(24)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
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       "     \"BokehJS does not appear to have successfully loaded. If loading BokehJS from CDN, this \\n\"+\n",
       "     \"may be due to a slow or bad network connection. Possible fixes:\\n\"+\n",
       "     \"</p>\\n\"+\n",
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       "     \"<li>use INLINE resources instead, as so:</li>\\n\"+\n",
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       "      Bokeh.embed.inject_css(\"https://cdn.pydata.org/bokeh/release/bokeh-0.12.4.min.css\");\n",
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       "       \"<li>use INLINE resources instead, as so:</li>\\n\"+\n",
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       "       \"output_notebook(resources=INLINE)\\n\"+\n",
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       "            var render_items = [{\"docid\":\"a9924ccd-9443-45f6-9360-fb660a2b9d68\",\"elementid\":\"14c9c1f6-d54b-4b97-abe8-d794984b15ba\",\"modelid\":\"aa931700-85b9-4890-afb3-ca516f6d5581\"}];\n",
       "            \n",
       "            Bokeh.embed.embed_items(docs_json, render_items);\n",
       "          };\n",
       "          if (document.readyState != \"loading\") fn();\n",
       "          else document.addEventListener(\"DOMContentLoaded\", fn);\n",
       "        })();\n",
       "      },\n",
       "      function(Bokeh) {\n",
       "      }\n",
       "    ];\n",
       "  \n",
       "    function run_inline_js() {\n",
       "      \n",
       "      if ((window.Bokeh !== undefined) || (force === true)) {\n",
       "        for (var i = 0; i < inline_js.length; i++) {\n",
       "          inline_js[i](window.Bokeh);\n",
       "        }if (force === true) {\n",
       "          display_loaded();\n",
       "        }} else if (Date.now() < window._bokeh_timeout) {\n",
       "        setTimeout(run_inline_js, 100);\n",
       "      } else if (!window._bokeh_failed_load) {\n",
       "        console.log(\"Bokeh: BokehJS failed to load within specified timeout.\");\n",
       "        window._bokeh_failed_load = true;\n",
       "      } else if (force !== true) {\n",
       "        var cell = $(document.getElementById(\"14c9c1f6-d54b-4b97-abe8-d794984b15ba\")).parents('.cell').data().cell;\n",
       "        cell.output_area.append_execute_result(NB_LOAD_WARNING)\n",
       "      }\n",
       "  \n",
       "    }\n",
       "  \n",
       "    if (window._bokeh_is_loading === 0) {\n",
       "      console.log(\"Bokeh: BokehJS loaded, going straight to plotting\");\n",
       "      run_inline_js();\n",
       "    } else {\n",
       "      load_libs(js_urls, function() {\n",
       "        console.log(\"Bokeh: BokehJS plotting callback run at\", now());\n",
       "        run_inline_js();\n",
       "      });\n",
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       "  }(this));\n",
       "</script>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "output_notebook()\n",
    "\n",
    "plot = figure(y_range=(0, .5))\n",
    "plot.scatter(x=range(1, 25), y=fields)\n",
    "show(plot)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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